In the right triangles with sides...

In the right triangles with sides (3,4,5) and (5,12,13), one side is just 1 less than the hypotenuse. Find all such integer-sided right triangles. [If you cannot do that, at least try to determine whether or not there are infinitely many of them.]

In the right triangles with sides (3,4,5) and (5,12,13), one side is just 1 less than the hypotenuse. Find all such integer-sided right triangles. [If you cannot do that, at least try to determine whether or not there are infinitely many of them.]

Thanks!

Since $\displaystyle c $ is odd and $\displaystyle c-b=1 $, this implies that $\displaystyle b $ is even, so $\displaystyle b=2mn $ and we know $\displaystyle c=m^2+n^2 $.